-LRB- CNN -RRB- -- The Williams sisters continued their march towards more Olympic success with three victories between them in London on Monday .

Fourth seed Serena romped into the third round of the women 's singles with a 6-2 6-3 win over Poland 's Ursula Radwanska , whose older sister Agnieszka she beat to win her fifth Wimbledon title earlier this month .

The American will next face Russian 13th seed Vera Zvonareva , who knocked out 2010 French Open champion Francesca Schiavone .

Zvonareva , the bronze medalist at Beijing four years ago , triumphed 6-3 6-3 .

`` It was tough conditions , a little windy . I 'm glad I was able to pull through , '' said Williams , who faces a possible quarterfinal against former world No. 1 Caroline Wozniacki or Slovakia 's Daniela Hantuchova as she seeks the only major title missing from her collection .

Her older sibling Venus , who is in the same half of the draw , bounced back from her early exits at the French Open and Wimbledon by thrashing Roland Garros runnerup Sara Errani 6-3 6-1 in her delayed first-round match .

`` Another gold medal would be amazing , '' said the 32-year-old , who won the singles title in 2000 along with the doubles , which she and Serena won again in 2008 .

`` I ca n't even imagine the feeling , I think my head would be too big and no one would even like me anymore . I 've got to get there first , I have two chances and I 'll go for it . ''

Venus will next play Canada 's Aleksandra Wozniak , who progressed into the second round by winning 6-2 6-1 against Marina Erakovic of New Zealand .

If she wins that game , Williams will play either German seventh seed Angelique Kerber or Hungary 's Timea Babos for a place in the quarterfinals .

That could mean a last-eight clash with world No. 1 Victoria Azarenka , who survived a second-set scare to beat 79th-ranked Romanian Irina-Camelia Begu 6-1 3-6 6-1 in her opening match on Centre Court .

The Belorussian , who lost to Serena in the Wimbledon semifinals , will next face Maria Jose Martinez Sanchez of Spain .

Serena and Venus also won their opening doubles match , beating Romania 's Sorana Cirstea and Simona Halep 6-3 6-2 to set up a clash with Kerber and Sabine Lisicki .

Lisicki also moved into round two of the singles , coming from behind to beat Tunisian teen Ons Jabeur -- ranked 297th -- and securing a match against Kazakhstan 's Yaroslava Shvedova .

The winner of that tie will likely face world No. 3 Maria Sharapova , who next plays Britain 's Laura Robson .

Former world No. 1s Kim Clijsters and Ana Ivanovic will meet in round three , while Czech sixth seed Petra Kvitova -- whose Wimbledon defense was ended by Serena Williams in the quarterfinals -- will take on Italy 's Flavia Pennetta .

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Serena and Venus Williams win their singles and doubles matches at the London Olympics at Wimbledon

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Americans could potentially meet in the singles semifinals of the grass-court tournament

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World No. 1 Victoria Azarenka wins her opening match and could play Venus in the quarterfinals

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Kim Clijsters , Ana Ivanovic and Petra Kvitova progress into round three of singles competition